Understanding and Mitigating Spurious Signal Amplification in Test-Time Reinforcement Learning for Math Reasoning

TL;DR

This paper identifies the problem of spurious signal amplification in test-time reinforcement learning for math reasoning and proposes DDRL, a framework that mitigates this issue through sampling, debiased advantage estimation, and off-policy refinement.

Contribution

The paper introduces DDRL, a novel framework that reduces spurious signals in TTRL by combining sampling, bias removal, and stable model updates, improving performance on math reasoning tasks.

Findings

DDRL outperforms existing TTRL methods on multiple benchmarks.

Spurious signals are amplified by group-relative advantage estimation.

Frequency-based sampling reduces ambiguity in training samples.

Abstract

Test-time reinforcement learning (TTRL) always adapts models at inference time via pseudo-labeling, leaving it vulnerable to spurious optimization signals from label noise. Through an empirical study, we observe that responses with medium consistency form an ambiguity region and constitute the primary source of reward noise. Crucially, we find that such spurious signals can be even amplified through group-relative advantage estimation. Motivated by these findings, we propose a unified framework, Debiased and Denoised test-time Reinforcement Learning (DDRL), to mitigate spurious signals. Concretely, DDRL first applies a frequency-based sampling strategy to exclude ambiguous samples while maintaining a balanced set of positive and negative examples. It then adopts a debiased advantage estimation with fixed advantages, removing the bias introduced by group-relative policy optimization. Finally, DDRL incorporates a consensus-based off-policy refinement stage, which leverages the rejection-sampled dataset to enable efficient and stable model updates. Experiments on three large language models across multiple mathematical reasoning benchmarks demonstrate that DDRL consistently outperforms existing TTRL baselines. The code will soon be released at https://github.com/yuyongcan/DDRL.